Searches have been carried out at a house in Viola Avenue, Stanwell, and a cordon remained in place.
The suspect is being held under Section 41 of the Terrorism Act 2000 and police have been granted a warrant of further detention, allowing them to question him until Saturday without charge.
Investigators are appealing for anyone who witnessed or filmed the incident, which started place shortly after 10pm on Saturday, to come forward.
Officers were first called to Viola Avenue in Stanwell, to reports of a man acting aggressively and shouting racist comments whilst carrying a baseball bat and a knife. Several vehicles were damaged.
Another call at 11.10pm reported that a man had been stabbed in a nearby Tesco car park.
Armed officers detained the 50-year-old shortly afterwards.
The victim sustained serious injuries to his hands, going into a McDonalds to seek help and being taken to hospital by ambulance.
He has undergone surgery and was discharged from hospital on Monday.
Detective Superintendent Karen Mizzi, from Surrey Police, said: “Patrols have been stepped up across Stanwell in order to provide assurances to those in the area specifically around mosques and increasing engagement with communities of all faiths, giving advice on how people and places can protect themselves.”
“Police are committed to tackling all forms of toxic extremist ideology, which has the potential to threaten public safety and security,” Det Supt Doak said. “Extreme right-wing investigations are pursued by our officers with the same level of resource and determination as other forms of extremist ideology.”
Greater Manchester Police have made several other arrests related to online comments and malicious communications linked to the Christchurch terror attack.
Anyone with information or footage of the Stanwell incident is asked to contact Surrey Police on 101, quoting reference number 19060857.
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